The viability of every cell in the human body depends upon an adequate supply of oxygen. Paradoxically, despite its role as the body's most important metabolite, oxygen is not stored in significant quantities by the body. Continuous and adequate transport of oxygen to the body cells is instead normally established by directing a constant flow of blood-laden oxygen from the lungs through the body's blood circulatory system to the individual body cells in need of oxygen. Interruption in the oxygen transport process for even brief periods of time can result in unconsciousness and death. Unfortunately, many otherwise salutory clinical or surgical procedures present the risk of such interruption, and the desirability of undertaking these clinical or surgical proceedings is dependent upon the ability of the attending surgical staff to obtain accurate, continuous real-time measurements of oxygen levels in the blood. If blood oxygen levels thus monitored drop dangerously, appropriate emergency procedures can be undertaken to protect the life of the patient.
One of the more practical methods for ascertaining the amount of oxygen in the blood involves determining the blood oxygen saturation level. The oxygen saturation level is a measure of the amount of oxygenated hemoglobin present in the bloodstream relative to all of the hemoglobin present in the bloodstream. Hemoglobin in turn is a conjugated protein which is present in red blood cells. Practically speaking, red blood cells are formed as bioconcave discs of approximately 10 micrometers diameter and commonly exist in densities of approximately five million red blood cells per cubic millimeter. It is known that red blood cells both scatter and transmit radiant energy incident thereon in amounts which vary as a function of the oxygen content of the hemoglobin in the cells. The differential absorption of radiant energy between oxygenated and non-oxygenated hemoglobin as radiant energy is transmitted through red blood cells furnishes a convenient basis for measuring oxygen saturation levels.
Oxygen saturation level measurements can be performed by utilizing an indwelling intravascular catheter which conducts radiant energy from an external light source to an in vivo measurement site and returns energy reflected or scattered back from the red blood cells to an external detector. Intravascular catheters of this type, known as optical catheters, generally include transmitting and receiving fiber optic light guides for respectively conducting radiant energy to and returning radiant energy from the in vivo measurement site. The transmitting fiber optic light guide has an inlet aperture connected to an LED or other light source while the receiving fiber optic light guide has an outlet aperture connected to a photodetector. The outlet aperture of the transmitting fiber optic light guide is commonly oriented in a co-planar relationship with the inlet aperture of the receiving fiber optic light guide. Radiant energy admitted to the in vivo measurement site through the outlet aperture of the transmitting fiberoptic light guide is both absorbed and back-scattered by the red blood cells in the vicinity of the in vivo measurement site, with the amount of absorption varying as a function of the oxygen content of the blood cell hemoglobin as described above. A portion of the radiation back-scattered from the blood, hereinafter simply referred to as "back-scattered radiation," enters the inlet aperture of the receiving fiber optic light guide and is driected to the photodetector where the intensity of the back-scattered radiation can be ascertained. Due to the variation in radiation absorption brought about by changes in the oxygen saturation level of the blood under test, the total amount of back-scattered radiation available for detection at the photodetector likewise varies as a function of oxygen saturation. The oxygen saturation level may thus be computed using the detected intensities of the radiation returned from the in vivo measurement site. One prior art equation employed for oxygen saturation level computations based on radiation intensity determinations is of the form: EQU S.sub.3 =A.sub.0 +A.sub.1 (I.sub.3 /I.sub.2)=A.sub.0 +A.sub.1 R.sub.3 ( 1)
where I.sub.2 represents the intensity of back-scattered radiation returned from the blood at wavelength .lambda..sub.2, I.sub.3 represents the intensity of back-scattered radiation returned at wavelength .lambda..sub.3. R.sub.3 is the ratio between I.sub.3 and I.sub.2 and A.sub.0 and A.sub.1 are empirically derived calibration coefficients. In the two-wavelength measuring system necessary to implement Equation (1), .lambda..sub.3 is usually an isosbestic wavelength, i.e., a wavelength at which little or no difference appears in the optical absorptance of oxygenated hemoglobin versus non-oxygenated hemoglobin, while .lambda..sub.2 is a non-isosbestic wavelength.
Inasmuch as the amount of radiation actually back-scattered from red blood cells at the in vivo measurement site represents a very small fraction of the total radiation transmitted to the in vivo measurement site, the intensity of back-scattered radiation received at the inlet aperture to the receiving fiber optic light guide is greatly influenced by many factors in addition to the differential absorption qualities of the oxygenated and non-oxygenated hemoglobin. For example, changes in the number of red blood cells, their location, size, shape and orientation can all affect the extent to which back-scattering occurs. Moreover, the blood under test flows past the in vivo measurement site in a pulsatile fashion, causing the tip of the optical catheter to move in an uncontrolled manner with respect to the blood vessel walls. Whenever a blood vessel wall appears in the near field of the catheter tip, a very large array of tightly-packed back-scattering blood cells is introduced into the measurement system. This cell packing phenomenon results in a significant variation in the distribution and number of back-scattering blood cells, producing substantial and wavelength-dependent changes in the intensities of radiation returned to the receiving fiber optic light guide. Wavelength-dependent radiation intensity fluctuations, of course, affect the overall accuracy of oxygen saturation level computations obtained from radiation-dependent equations such as Equation (1).
In order to compensate for inaccuracies in Equation (1) attributable to uncontrollable changes in the aforementioned physiologic parameters, new equations have been developed. For example, U.S. Pat. No. 3,847,483 issued to Shaw, et al., proposes a two-wavelength measuring system in which oxygen saturation levels can be determined according to the relationship: ##EQU1## where I.sub.1 and I.sub.2 are the back-scattered radiation intensities detected at wavelengths .lambda..sub.1 and .lambda..sub.2 respectively and B.sub.0, B.sub.1, B.sub.2, C.sub.0, C.sub.1 and C.sub.2 are empirically derived calibration or weighting coefficients. Neither .lambda..sub.1 and .lambda..sub.2 need be isosbestic wavelengths. Dividing both the numerator and denominator of Equation (2) by 1/I.sub.1 yields: ##EQU2## where R.sub.2 is the ratio between I.sub.2 and I.sub.1. As can be seen, Equation (3) attempts to offset errors in oxygen saturation level calculations by utilizing intensity ratios to minimize the effect of fluctuations in the intensity measurements. However, as noted in U.S. Pat. No. 4,114,604 issued to Shaw, et al., oxygen saturation level measurements determined in accordance with Equation (3) to some extent remain a function of individual light intensities as well as the aforementioned physiologic phenomena such as blood flow velocity, hematocrit, pH and pCO.sub.2. As a more accurate alternative to Equations (1) and (2), U.S. Pat. No. 4,114,604 offers yet another equation, i.e.: ##EQU3## where I.sub.1, I.sub.2 and I.sub.3 are intensities of back-scattered radiation respectively detected at wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.3 and normalized against a reference light intensity, B.sub.0, B.sub.1, B.sub.2 and B.sub.3 are weighting factors or coefficients and C.sub.0, C.sub.1, C.sub.2 and C.sub.3 are likewise weighting factors or coefficients. Substituting R.sub.1 for the ratio I.sub.1 /I.sub.2 and R.sub.3 for the ratio I.sub.3 /I.sub.2 yields: ##EQU4##
In operation, the apparatus disclosed in U.S. Pat. No. 4,114,604 for implementing Equation (5) is a three-wavelength oximeter which transmits radiation to the in vivo measurement site at wavelengths of approximately 670 nanometers, 700 nanometers and 800 nanometers. These wavelengths were empirically selected on the basis of data taken from a large number of in vitro studies conducted on anesthetized experimental animals, human volunteers and clinical patients undergoing surgery and intensive care. For each of the wavelengths selected, the ratio of back-scattered intensities as a function of actual oxygen saturation level has been plotted, using the physiologic parameter of hematocrit as a variable. This plot is reproduced in FIG. 1, with R.sub.1 representing the ratio of back-scattered intensities at 670 nm and 700 nm and R.sub.3 representing the ratio of back-scattered intensities at 800 nm and 700 nm. Each of the ratios R.sub.1 and R.sub.3 has been observed and plotted at respective hematocrit values of 0.25 and 0.45. The latter values are respectively near the lower and upper extremes of the range of hematocrit values of interest. From the graph of FIG. 1, it can be seen that R.sub.3 is relatively independent of changes in hematocrit value at oxygen saturation levels of approximately 36% but varies greatly with changes in hematocrit value throughout the upper regions, i.e., the 60%-90% regions, of the oxygen saturation level range. On the other hand, R.sub.1 is relatively independent of changes in hematocrit value at oxygen saturation levels of approximately 90% but varies widely with changes in the hematocrit value throughout the lower regions of interest in the oxygen saturation level range. Similar behavior of R.sub.1 and R.sub.3 has been observed with respect to changes in blood pH, blood pCO.sub.2 and like parameters.
Upon reflection, it should be evident that error in the computed oxygen saturation level resulting from changes in physiologic parameters can be minimized by weighting Equation (5) in favor of that ratio of back-scattered radiation which exhibits minimum variation as a function of the given physiologic parameter in the oxygen saturation range of interest. Conversely, Equation (5) should be weighted most heavily against that ratio of back-scattered radiation which exhibits maximum variation as a function of the given physiologic parameter in the oxygen saturation range of interest. If the aforementioned weighting is performed, the value obtained from Equation (5) for any given set of detected back-scattered radiation ratios will depend primarily on the most stable ratio in the set. Actual selection of proper factors or coefficients in Equation (5) can be carried out empirically by substituting coefficient values until the differential of computed oxygen saturation level with respect to each ratio of back-scattered radiation approximates zero at a point where the remaining ratio of back-scattered radiation experiences the least variation in response to change in the physiologic parameter.
It will be recalled from FIG. 1 that the ratio R.sub.3 varies minimally while the ratio of R.sub.1 varies greatly in response to changes in hematocrit at oxygen saturation levels ranging between 25% and 45%. In contrast, the variation of R.sub.1 as a function of hematocrit is minimal while that of R.sub.3 is large at oxygen saturation levels ranging between 85% and 100%. Errors introduced into the computation of oxygen saturation level as a result of changes in the unmeasured hematocrit will thus be significantly reduced if Equation (5) is made to depend most heavily upon R.sub.3 in the range of 25% to 45% OS and on R.sub.1 in the range of 85% to 100% OS. The required conditions can be established by selecting the Equation (5) weighting factors such that the derivative of Equation (5) with respect to R.sub.1 approximates zero in the range of 25% to 45% OS, i.e.: ##EQU5## The derivative of Equation (5) with respect to R.sub.3 should approximate zero in the range of 85% to 100% OS, i.e., ##EQU6## When the latter constraints are simultaneously satisfied, as illustrated in FIG. 2, errors in computations of oxygen saturation levels based on measurements of intensity ratios will tend to be minimized in relation to changes of non-measured but wavelength-dependent blood characteristics other than oxygen saturation level.
Although use of Equation (5) together with appropriate weighting coefficients improves the accuracy of oxygen saturation level computations, additional empirical data has revealed that the aforementioend weighting constraints as applied to Equation (5) cannot be completely satisfied. In particular, the relationship expressed in Equation (6) is easier to achieve than that expressed in Equation (7) and hence the empirically determined coefficients tend to weight R.sub.1 more heavily than R.sub.3. Inasmuch as variations in R.sub.1 brought about by changes in the non-measured hematocrit tend to decrease as the oxygen saturation level increases, the weighting bias in favor of R.sub.1 will enhance the accuracy of Equation (5) at the high end of the oxygen saturation range. At lower levels of oxygen saturation, variation in the value of R.sub.1 due to changes in unmeasured hematocrit increase and the inability to completely satisfy Equation (7) leaves Equation (5) more vulnerable to error introduced by unaccountable shifts in R.sub.1.